Given that n is a positive prime number. Determine analytically all possible n such that 2n + n2 is a prime number.
(In reply to needs a second attempt
The fundamental tenets inclusive of the problem under reference
may not be satisfied for all odd numbers n.
For example, when n= 11; we obtain, 2^11 + 11^2 = 2169 which is divisible by 9.
It may also be noted that according to conditions of the problem, n is a positive prime number.